Once all the BTC are mined, what will be the effect of the gradual decline in the number of BTC due to being lost, etc.

My theory is that once all BTC are mined, it will actually start losing value (I know, the law of scarcity says otherwise).

I view the next few decades of altcoins as people shifting from coin to coin because as long as you can mine them, people will be interested. Once it is too difficult to mine, people will move to the new coin that gives them hope. I'm not saying BTC will disappear, but just that the focus will be on the next altcoin that gives people the impression that they can mine some and be millionaires.

Except that when it starts getting so difficult that people start turning off all of their miners, the global hashrate will drop and therefore the difficulty will also drop. Which will encourage people to start mining again.

I rather doubt there will be many alt-coins left when the last bitcoin has been mined. Either bitcoin has established itself as a viable currency/payment option and the altcoins have fallen into disuse or it hasn't and nobody will care anyway.

Right now almost all the value in all the coins lies in speculation. Bitcoin is the only coin that you can actually buy stuff with and thus the only coin that has something approaching to actual value. I expect that once everything is settled down the only coins left will be the ones that are actually used for payment instead of speculation.

You mean in 2140 when all the coins have been mined? It we still have bitcoins in 100 years it will be as an archaic museum piece that is kept around for historical reasons. BitCoins are a computer program, what might be around is the program decedent of BitCoin that won't look anything like the BitCoin of today, and will probably have been replaced by something revolutionary that will make BitCoins look as silly as the money of today.

The decline in supply will increase the usd value. But not by much imo.

You can never truly lose any of the 21m btc, depends on mining possibly on dead addresses. Pooled computing or asic power will likely be so powerful by then people will start calculating private keys for the lost bitcoins, similar to what people are doing for vanity addresses today.

Those still in the economy would have gradually updated the protocol and their wallets to use stronger private keys to counter the miners.